In order to research the vibration law of electrostatic suspension systems in the vertical direction, the mathematical model of nonlinear differential equation is established. A series of simulation is carried out. The results show that the solution of the differential equation is a periodic function. The amplitude becomes bigger with the original velocity increasing. The period becomes smaller with the original velocity increasing. The numerical methods are presented to derive the amplitude and the frequency, and the results correspond to the simulation. The condition is pointed out when simple harmonic vibration arises. The expressions of the amplitude and the period of simple harmonic vibration are derived respectively, and the results are the same with simulation. This study is helpful to get to know the vibration characteristics of the electrostatic suspension system. The external disturb should be controlled to lower the amplitude and the frequency of the vibration.

In order to research the vibration law of electrostatic suspension systems in the vertical direction, the mathematical model as a nonlinear differential equation is established. A series of simulation is carried out. The results show that the solution of the differential equation is a periodic function. The amplitude becomes bigger with the original velocity increased. The period becomes smaller with the original velocity increasing. The numerical methods are presented to derive the amplitude and the frequency, and the results coincide with that of the simulation. The condition during which the simple harmonic vibration arises is pointed out. The expressions for the amplitude and the period of simple harmonic vibration are derived respectively, and the results are the same with that of the simulation. This study is helpful for researching the vibration characteristics of the electrostatic suspension system. The external disturb should be controlled to lower the amplitude and the frequency of the vibration.